Partial differential equations : an introduction
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Bibliographic Information
Partial differential equations : an introduction
（Mathematische Leitfäden）
B.G. Teubner, 1977, c1964
2nd ed
- Other Title
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Partielle Differentialgleichungen
- Uniform Title
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Partielle Differentialgleichungen
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Translation of Partielle Differentialgleichungen
Bibliography: p. [256]
Includes index
Description and Table of Contents
Table of Contents
1. Examples.- 1. Introduction.- 2. The Wave Equation.- 3. The Potential Equation.- 4. The Heat Equation.- 2. Classification into Types, Theory of Characteristics, and Normal Form.- 1. Differential Equations of the First Order.- 2. Systems of Differential Equations of the First Order.- 3. On the Necessity of Classification Into Types.- 3. Questions of Uniqueness.- 1. Elliptic and Elliptic-Parabolic Type.- 2. Parabolic Type.- 3. Hyperbolic Type.- 4. Mixed Type.- 4. Questions of Existence.- 1. Equations of Hyperbolic Type in Two Independent Variables.- 2. Boundary and Initial-Value Problems for Equations of Hyperbolic and Parabolic Type in Two Independent Variables.- 3. Equations of Elliptic Type.- 4. Weyl's Lemma for Equations of Elliptic Type.- 5. Simple Tools from Functional Analysis Applied to Questions of Existence.- 1. Auxiliary Tools.- 2. Schauder's Technique of Proof for Existence Problems in Elliptic Differential Equations.- 3. The Regular Eigenvalue Problem.- 4. Elliptic Systems of Differential Equations.- Solutions.
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